2. Agents that reason logically(Logical
agents)
• A Knowledge based Agent
• The Wumpus world environment
• Representation, Reasoning and Logic
• Logics – An Introduction
• Propositional Logic
• An Agent for the wumpus world – Propositional
Logic
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3. Abilities KB agent
• Agent must be able to:
• Represent states and actions,
• Incorporate new percepts
• Update internal representation of the world
• Deduce hidden properties of the world
• Deduce appropriate actions
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4. Agents that Reason Logically
• Logical agents have knowledge base, from
which they draw conclusions
• TELL: provide new facts to agent
• ASK: decide on appropriate action
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5. Sample: Wumpus World
• Show original wumpus game
• goal is to shoot wumpus
• example of logical reasoning
• Our version:
• Find gold, avoid wumpus, climb back out of
cave
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6. A Wumpus Agent
• Agent does not perceive its own location (unlike
sample game), but it can keep track of where it
has been
• Percepts:
• Stench – wumpus is nearby
• Breeze – pit is nearby
• Glitter – gold is here
• Bump – agent has just bumped against a wall
• Scream – agent has heard another player die
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7. Wumpus Agent
• Actuators:
• Forward, Turn Left, Turn Right
• Grab (gold)
• Shoot (shoots arrow forward until hits
wumpus or wall)
• agent only has one arrow
• Climb (exit the cave)
• Environment:
• 4x4 grid, start at (1,1) facing right
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8. Wumpus Agent
• Death
• Agent dies if it enters a pit or square with
wumpus
• Goal: get gold and climb back out. Don’t die.
• 1000 points for climbing out of cave with gold
• 1 point penalty for each action taken
• 10,000 point penalty for death
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9. Some complex reasoning examples
• Start in (1,1)
• Breeze in (1,2) and (2,1)
• Probably a pit in (2,2)
• Smell in (1,1) – where can you go?
• Pick a direction – shoot
• Walk in that direction
• Know where wumpus is
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10. Another example solution
No perception 1,2 and 2,1 OK B in 2,1 2,2 or 3,1 P?
Move to 2,1 1,1 V no P in 1,1
Move to 1,2 (only option)
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11. Example solution
S and No S when in 2,1 1,3 or 1,2 has W
1,2 OK 1,3 W
No B in 1,2 2,2 OK & 3,1 P
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12. AI Models and Pr opositional
Logic
•The Role of a Model
•Represent The Environment
•Assimilate Knowledge
•Learning
•Simulation
•Inference
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13. Models
• If we are going to create programs that
are intelligent, then we need to figure out
how to represent models
• They allow us to predict certain things
about the future.
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14. The Role of a Model
• Represent the environment
• Provide a structure for the assimilation of
new knowledge
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15. Represent The Environment
• Features in the environment must be
represented as features in the model
• They should be able to act in the model just as
they do in the environment
• Needs to be able to represent both long term
qualities of the environment and short term
states.
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16. Assimilate Knowledge
• A model of the world allows an agent to
organize new information in the context of
what it already knows and draw
conclusions.
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17. Learning
• An AI agent may start ready programmed
with knowledge, or it may have to learn it
from experience
• The model may change in response to
new experiences.
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18. Simulation
• Simulate the real environment to test
potential actions.
• The model needs to accept simulated
sensory input and it needs to feed
simulated actions back in without actually
making those actions in reality
• It needs an imagination
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22. Ontological and Epistemological Assumptions
• ontological assumption :It is understood in connection to the
logic of functioning of the agent.
- question is: “What does the agent do?” This means discussing
both what the agent is and what its behavior constitutes of.
• Epistemological assumptions: It consider the nature of
knowledge.
- question is: “On what knowledge does the agent base its
actions?” It is important to discuss the origins of knowledge as well
as concepts such as learning and memory.
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24. The use of logic
• A logic: formal language for representing information,
rules for drawing conclusions
• Two kinds of logics:
• Propositional Logic
• Represents facts
P∧Q ⇒ R
• First Order Logic
• Represents facts, objects, and relations
∀x Cat ( x) ⇒ Mammal ( x)
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25. Entailment
• One thing follows from another
KB |= α (knowledge base entails alpha)
• KB entails sentence α if and only if α is true in worlds where
KB is true.
Ε.g. x+y=4 entails 4=x+y
• Entailment is a relationship between sentences that is based
on semantics.
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26. Propositional Logic
• Represents facts as being either true or false
• Formally represented by a letter, e.g. P or Q.
• Actually refer to facts about the environment, e.g.
the speed limit in town is 30mph
• Single facts can be combined into sentences using
Boolean operators
• These sentences, if true, can become facts in the KB.
• A KB is said to entail a sentence if it is true in the
KB
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27. Logic consists of
• Logical constants: true, false
• Proposition symbols: P, Q, R, ...
• Logical connectives: & (or ^), ∨, ¬, →, ↔
• Parentheses: ( )
• Propositional logic is an extremely simple
representation
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28. Basic symbols
• Expressions only evaluate to either “true” or “false.”
• P “P is true”
• ¬P “P is false” negation
• PVQ “either P is true or Q is true or both” disjunction
• P^Q “both P and Q are true” conjunction
• P => Q “if P is true, the Q is true” implication
• PQ “P and Q are either both true or both false” equivalence
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30. Syntax rules for propositional logic
• The constants true and false are propositions by
themselves.
• A proposition symbol such as P or Q is a
proposition by itself.
• Wrapping parentheses around a proposition
produces proposition.
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31. Ambiguity
The grammar can be ambiguous, for example:
P & Q ∨ R.
It is best to use parentheses to eliminate ambiguity.
When ambiguity is present, we resolve it with
operator precedence:
(highest) : ¬ ,& ,∨ ,⇒ , ⇔ (lowest)
For example: ¬P ∨ Q & R )⇒ S
is equivalent to: ((¬ P) ∨ (Q & R)) ⇒ S
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32. Limitations of Propositional Logic
1. It is too weak, i.e., has very limited expressiveness:
• Each rule has to be represented for each situation:
e.g., “don’t go forward if the wumpus is in front of you” takes 64 rules
2. It cannot keep track of changes:
• If one needs to track changes, e.g., where the agent has been before then
we need a timed-version of each rule. To track 100 steps we’ll then need
6400 rules for the previous example.
Its hard to write and maintain such a huge rule-base
Inference becomes intractable
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41. Determining action based on knowledge
A1, 2 ∧ W1,3 ∧ Forward A ⇒ Shoot
A1, 2 ∧ P ,3 ∧ Forward A ⇒ ¬Forward
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• Propositional logic cannot answer well the question
“What action should I take?”
• It only answers “Should I take action X?”
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42. Propositional logic seems inefficient
• Rule: “Shoot if the wumpus is in front of you”
• 16 x 4 = 64 rules for the 4x4 grid
• Ditto for pits
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43. First-order logic to the rescue
• Uses variables to represent generalities
• Can reduce rules significantly
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